US7711066B2 - Uniform channel decomposition for MIMO communications - Google Patents
Uniform channel decomposition for MIMO communications Download PDFInfo
- Publication number
- US7711066B2 US7711066B2 US11/718,506 US71850605A US7711066B2 US 7711066 B2 US7711066 B2 US 7711066B2 US 71850605 A US71850605 A US 71850605A US 7711066 B2 US7711066 B2 US 7711066B2
- Authority
- US
- United States
- Prior art keywords
- matrix
- channel
- precoder
- mimo
- decomposition
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
- H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
- H04L1/0618—Space-time coding
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
- H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
Definitions
- the invention is generally related to the field of communications, and, more particularly, to communications over multiple-input-multiple-output channels.
- MIMO multiple-input-multiple-output
- SISO single-input-single-output
- MIMO-based communications may help, for example; to resolve the bottleneck problem limiting traffic capacity in future Internet-intensive wireless networks.
- Many researchers also believe that MIMO-based technology is poised to penetrate large-scale, standards-driven commercial wireless products and networks such as broadband wireless access systems, wireless local area networks (WLAN), and third-generation (3G) as well as fourth-generation (4G) networks.
- WLAN wireless local area networks
- 4G fourth-generation
- MIMO communications systems take advantage of random channel fading and, when possible, multipath delay spread to increase channel capacity. This is accomplished by combining at a receiver the signals transmitted from multiple transmitting antennas to multiple receiving antennas so as to increase quality in terms of the bit-error rate (BER) or the data rate (bits per second).
- BER bit-error rate
- bits per second bits per second
- Bit allocation not only complicates the needed modulation but also reduces capacity due to the granularity of a finite symbol constellation corresponding to the coding scheme employed.
- the same symbol constellation is used for each subchannel, as for example according to the HIPERLAN/2 and IEEE 802.11 standards for WLANs, then more power should be allocated to the poorer or less robust subchannels.
- Using the same constellation for each subchannel can lead to significant performance degradation.
- the conventional linear transceiver designs therefore, pose a tradeoff between channel capacity and performance in terms of BER if the complexity of bit allocation is to be avoided. It follows that there is a need for an effective and efficient alternative to conventional linear transceiver designs.
- the present invention provides systems and method for implementing a uniform channel decomposition scheme.
- the uniform decomposition scheme decomposes a MIMO channel into a plurality of subchannels over which communication signals are conveyed.
- One embodiment of the invention is a multi-input-multi-output (MIMO) communications system for conveying signals over a MIMO channel.
- the system can include a precoder for precoding a signal based upon a uniform channel decomposition scheme.
- the system can further include a transmitter in communication with the precoder for conveying the precoded signal over a subchannel of the MIMO channel.
- a system for conveying signals over a MIMO channel can include a transmitting unit having an array of transmitting antennas and a uniform channel decomposition module for decomposing a transmission channel into multiple subchannels having equal capacities over which multiple communications signal are conveyed.
- the system also can include a receiving unit having an array of receiving antennas for receiving the multiple communications signals.
- Another embodiment of the invention is a method for conveying signals over a MIMO channel.
- the method can include precoding a signal based upon a uniform channel decomposition scheme.
- the method further can include transmitting the precoded signal over a subchannel of the MIMO channel.
- FIG. 1 is a schematic diagram of a multiple-input-multiple-output communications system that implements a uniform channel decomposition, according to one embodiment of the invention.
- FIG. 2 is a schematic diagram of a multiple-input-multiple-output communications system that implements a uniform channel decomposition, according to another embodiment of the invention.
- FIG. 3 is a schematic diagram of a multiple-input-multiple-output communications system that implements a dual form of the uniform channel decomposition, according to still another embodiment of the invention.
- FIG. 4 is a schematic diagram of a MIMO-OFDM transmitter, according to yet another embodiment of the invention.
- FIG. 5 is a schematic diagram of a MIMO-OFDM receiver, according to still another embodiment of the invention.
- FIG. 6 is a schematic diagram of a matrix transformation based on a geometric mean decomposition according to one aspect of the invention.
- the invention provides a uniform channel decomposition scheme for multiple-input-multiple-output (MIMO) communications systems.
- the uniform channel decomposition scheme decomposes a MIMO channel into multiple subchannels such that each subchannel has the same, or approximately the same, capacity in the sense that the output of each subchannel has the same signal-to-noise plus interference ratio (SNIR). As explained herein, this affords an opportunity to simplify modulation and demodulation as well as coding and decoding of transmitted signals.
- the channel decomposition effected by the uniform channel decomposition scheme also can decompose a MIMO channel into multiple subchannels that are strictly capacity lossless.
- the uniform channel decomposition scheme also can enable the MIMO communications system to achieve maximal diversity gain. UCD can achieve an optimal tradeoff between diversity gain and multiplexing gain with relatively low processing complexity.
- the uniform channel decomposition scheme can be implemented in different forms.
- the invention also can be applied to a variety of communication protocols, including those based on orthogonal frequency division multiplexing (OFDM), code division multiple access (CDMA), time division multiple access (TDMA), and the global system for mobile communications (GSM).
- OFDM orthogonal frequency division multiplexing
- CDMA code division multiple access
- TDMA time division multiple access
- GSM global system for mobile communications
- the systems include voice and data systems such as those utilizing digital telecommunications protocols and those utilizing digital subscriber lines (DSL).
- DSL digital subscriber lines
- the devices with which the invention can be implemented include, for example, cellular phones, personal digital assistants (PDA), and computing devices such as laptop computers.
- FIG. 1 schematically illustrates a UCD-based MIMO communications system 100 according to one embodiment of the invention.
- the communications system 100 illustratively comprises a transmitting unit 105 and a receiving unit 110 , the transmitting unit conveying information-carrying signals to the receiving unit over a transmission medium, or MIMO channel 115 .
- the transmitting unit 105 illustratively connects to a plurality of transmitting antennas 145 that simultaneously transmit differently encoded signals, or symbols.
- the receiving unit 110 illustratively connects to a plurality of receiving antennas 146 that simultaneously receive the different signals, or symbols, conveyed via the channel 115 .
- the transmitting unit 105 illustratively comprises a processing unit 135 implemented in dedicated hardwired circuitry and/or machine-readable code configured to be processed by logic-based circuitry.
- the processing unit 135 samples input signal S(t) and maps sampled bit sequences into a vector comprising corresponding symbols x k .
- the plurality of transmitting antennas 145 comprises M t antennas, and the processing unit 135 generates M t symbols, where the i-th symbol, x k (i) , is conveyed as a signal transmitted by the i-th transmitting antenna.
- each x k (i) , 1 ⁇ i ⁇ M t , symbol is a complex quadrature amplitude modulation (QAM) symbol.
- QAM quadrature amplitude modulation
- the symbols can be coded according to any other scheme, including quadrature phase shift keying (QPSK), M-ary phase shift keying (MPSK), cross-QAM, and offset-QPSK, for example.
- QPSK quadrature phase shift keying
- MPSK M-ary phase shift keying
- cross-QAM cross-QAM
- offset-QPSK offset-QPSK
- the transmitting unit 105 further includes a uniform channel decomposition (UCD) module 140 that effects the UCD scheme described more particularly below.
- the UCD module 140 comprises a precoder, implemented in hardwired circuitry and/or machine-readable code, which precodes the symbols x k in accordance with the UCD scheme prior to their conveyance via the Channel 115 to the receiving unit 110 .
- the UCD module 140 effectively decomposes the channel 115 into multiple subchannels, each having the same, or substantially the same, capacity as each of the other subchannels. Equivalently, each of the multiple subchannels decomposed according to the UCD scheme has an identical, or nearly identical, SNIR.
- the UCD scheme is now described in the context of the channel 115 , which is characterized herein as a frequency-selective channel.
- the channel can be represented by an M t ⁇ M r complex matrix, H ⁇ M t ⁇ M r , of rank K.
- Each element of the complex matrix, H denotes a fading channel coefficient.
- a 2 ⁇ 2 MIMO channel characterized by inter-symbol interference (ISI) and spatial correlation can be modeled with the following matrix:
- H ⁇ ( t ) R r 1 / 2 ⁇ [ h 11 ⁇ ( t ) h 12 ⁇ ( t ) h 21 ⁇ ( t ) h 22 ⁇ ( t ) ] ⁇ R t 1 / 2 , 0 ⁇ t ⁇ ( L - 1 ) ⁇ T , ( 1 )
- R t and R r quantify the spatial correlations of the channel fading.
- h ij denotes the channel link between the j-th transmitter antenna and the i-th receiver antenna
- L denotes the channel link
- T represents the sampling period.
- a more general frequency-selective channel can be represented by a spatial-time channel with larger dimensionality.
- the x is an L ⁇ 1 vector of complex elements, x ⁇ L ⁇ 1 , representing the information symbols precoded by a linear precoder F ⁇ M r ⁇ L .
- the vector y is an M r ⁇ 1 vector of complex elements, y ⁇ M r ⁇ 1 , representing the received signal.
- the matrix H ⁇ M t ⁇ M r is the rank K channel matrix, the (i,j)-th elements of which denote the fading coefficient between the j-th transmitting antenna and the i-th receiving antenna.
- Tr ⁇ • ⁇ denotes the trace of a matrix.
- the capacity of the channel 115 is
- C IT is the charnel capacity of an “informed transmitter.”
- Each of the diagonal elements, ⁇ k ( ⁇ ) can be determined from the following equation based on the known “water filling” technique:
- ⁇ k ⁇ ( ⁇ ) ( ⁇ - ⁇ ⁇ H , k 2 ) + , ( 7 ) with ⁇ being chosen such that
- the conventional linear precoder, F can be used to obtain a conventional linear transceiver design that is, in an information-theoretic sense, optimal.
- a conventional linear transceiver design that is, in an information-theoretic sense, optimal.
- the resulting conventional linear transceiver is typically characterized by multiple subchannels that each have very different SNRs. This gives rise to particular difficulties with respect to the subsequent modulation/demodulation and coding/decoding procedures that must be utilized with conventional linear transceivers.
- One aspect of the UCD scheme of the present invention is the implementation of a precoding technique that yields a modified precoder, ⁇ tilde over (F) ⁇ , superior to conventional precoders, F.
- the precoding procedure can, in a strictly lossless sense, decompose a MIMO channel into multiple subchannels whose capacities in terms of a SNIR, as noted above, are identical or nearly so.
- the UCD scheme can ease the computational burden of modulation/demodulation and coding/decoding by obviating the need for bit allocations.
- channel throughput and bit-error rates (BERs) can be simultaneously optimized using the UCD scheme.
- a computationally efficient and numerically stable algorithm for effecting the decomposition reflected in equation 9 is provided below.
- the UCD is accomplished using a precoder matrix that is a modification of a conventional precoder matrix.
- the first term on the left-hand side of equation 10, V accordingly is the conjugate transpose of V*.
- ⁇ k ⁇ ( ⁇ ) ( ⁇ - ⁇ ⁇ H , k 2 ) + .
- L ⁇ K matrix, ⁇ is one step leading to the UCD.
- introduction of ⁇ provides several distinct advantages. Firstly, however, the design of ⁇ is described.
- Precoding transmitted signals using the precoder matrix, ⁇ tilde over (F) ⁇ gives rise to the following virtual channel, which mathematically represents the channel over which the signals are conveyed:
- the following augmented matrix can be obtained from the representation of the virtual channel, where ⁇ is the ratio of the variance in noise in the channel, ⁇ z 2 , to the variance within the transmitted signals, ⁇ x 2 ; that is,
- G a [ U ⁇ ⁇ ⁇ * ⁇ ⁇ I L ] . ( 12 )
- a semi-unitary matrix ⁇ L ⁇ K is found such that a standard QR decomposition of G a yields an upper triangular matrix having equal diagonal elements. This is more particularly demonstrated by rewriting the augmented matrix, G a , as follows:
- G a [ U ⁇ [ ⁇ 0 K ⁇ ( L - K ) ] ⁇ ⁇ 0 * ⁇ ⁇ I L ] , ( 13 ) where ⁇ 0 ⁇ L ⁇ L is a unitary matrix.
- the matrix ⁇ is formed from the first K columns of the matrix ⁇ 0 .
- the augmented matrix G a can be further rewritten as
- the middle term of the right-hand side of the equation can be decomposed according to a geometric mean decomposition GMD, which follows from the theorem, above.
- the decomposition yields the following matrix:
- Equation 15 Given the singular-value decomposition (SVD) of H and the “water filling” level ⁇ 1/2 , only the GMD of equation 15 need be calculated.
- the desired linear precoder, ⁇ tilde over (F) ⁇ V ⁇ 1/2 ⁇ *, follows directly from the GMD.
- the term ⁇ comprises the first K columns of P* J .
- Q G a u U[ ⁇ 0 K ⁇ (L-K) ] ⁇ tilde over ( ⁇ ) ⁇ ⁇ 1 Q 1 Q 2 . . . Q L-1 . (26)
- ⁇ k ⁇ ( ⁇ ) ( ⁇ - ⁇ ⁇ H , k 2 ) + .
- nulling vectors are determined so that nulling and cancellation can be performed on any signal precoded by the linear precoder ⁇ tilde over (F) ⁇ .
- FIG. 2 schematically illustrates an array-to-array communications system 200 which operatively performs the UCD scheme, according to one particular embodiment.
- the system 200 comprises a transmitting unit 205 connected to a plurality of transmitting antennas 245 and a receiving unit 210 connected to a plurality of receiving antennas 246 for transmitting and receiving, respectively, encoded signals over a transmission medium or MIMO channel 215 .
- the transmitting unit 205 illustratively includes a processor 220 that performs the matrix operations described previously using a linear matrix precoder 225 .
- the processor 220 can be implemented in dedicated hardwired circuitry or in machine readable code configured to run on an application-specific or general-purpose computing device.
- the processing unit can be implemented in a combination of hardwired circuitry and machine-readable code.
- the hardwired circuitry can, for example, comprise input/output (I/O) interfaces, one or more microprocessors and/or digital signal processors (DSPs), and memory elements.
- the machine-readable code can comprise, for example, programming logic to provide signal processing functions such as sampling, encoding, and other processing functions known to those of ordinary skill in the art.
- An input signal, S(t) is provided as an input to the processing unit 220 .
- some of the functions, hardwired circuitry, and/or machine-readable code embodied in the processor 220 can be located apart from the other illustrated components of the transmitting system 205 .
- the functions performed by the processor 220 can be implemented in discrete components within or external to the transmitting system 205 .
- the M t symbol sequences drive identical, or substantially identical, pulse-shape filters g(t), such as filter 230 .
- the resultant shaped signals are then upconverted by upconverters 240 , to an RF carrier frequency, ⁇ 0 , and transmitted across the transmission medium 215 using a plurality of transmitting antennas 245 .
- transmission medium 215 comprises a quasi-static fading channel, which as previously described can be mathematically represented by the channel matrix, H.
- H the transmitted signals represented by row vectors, H
- M t is the number of transmit antennas
- M r is the number of receive antennas.
- reference to a channel is, again, to be understood to mean an M t ⁇ M r matrix, H, whose elements are channel coefficients as described above.
- interference in the transmission medium 215 such as co-channel interference, is represented by the diagonal arrows from transmitting system 205 to the receiving system 210 .
- filtering, downconverting, and sampling can be performed in discrete components or in integrated components at the receiving unit 210 or at one or more components located external to the receiving unit.
- the functions can be implemented in hardwired circuitry, machine-readable code, or a combination of circuitry and code.
- the sampled signals are illustratively supplied to signal extractor or detector 265 .
- the signal extractor or detector 265 is preferably embodied as a decision feedback equalizer, such as one based on the minimum mean-squared-error vertical Bell Labs layered space-time (MMSE-VBLAST) architecture familiar to those of ordinary skill in the art.
- the VBLAST detector cancels out known interference prior to signal detection.
- a particular embodiment of the communication 200 in which the decision feedback equalizer is implemented with a VBLAST detector is referred to herein as a UCD-VBLAST system.
- Combining the UCD scheme implemented by the precoder 225 of the processor 220 with a detector such as the MMSE-VBLAST yields particular advantages. Beyond decomposing the transmission channel into multiple subchannels having identical, or nearly identical, channel capacities, the combination mitigates or eliminates the need for bit allocation. The combination also mitigates or eliminates the inherent zero-forcing aspect that typically accompanies the use of a conventional zero-forcing VBLAST architecture or zero forcing algorithm and that can cause significant capacity loss, particularly for signals characterized by low SNRs.
- the CSIT can be obtained through feedback from the receiver.
- Conventional FDD systems are subject to errors if the feedback is not frequently updated.
- the present invention there is no need to assume a known CSIT.
- the CSIT, ⁇ need not be precise, even though the channel matrix, H, characterizing the transmission medium 215 is known at the receiving system 210 .
- the receiving system 210 can be assumed to the CSIT, ⁇ , since it is the feedback, albeit delayed, of the CSIR.
- the above-described UCD-VBLAST can be made robust against error in the CSIT.
- the particular embodiment is referred to herein as a robust UCD-VBLAST scheme.
- the precoder 225 of the processor 220 at the transmitting system 205 calculates the precoder, ⁇ tilde over (F) ⁇ , as previously described, but here the precoder 225 performs the calculation based on the CSIT, ⁇ .
- the resulting equivalent channel yields
- the processor of the receiving system 210 can apply the algorithm of an optimally ordered MMSE-VBLAST detector. Since the receiving unit 210 has perfect knowledge of the matrix G, the robust UCD-VBLAST scheme performs at least as well as an open-loop MMSE-VBLAST scheme even if the CSIT is not perfectly accurate. Accordingly, the robust MMSE-VBLAST scheme is particularly robust against CSIT errors.
- a dual form of the UCD scheme is obtained by reversing the roles of the transmitter and receiver.
- ⁇ ij
- 2 the SNIR representation is
- FIG. 3 schematically illustrates a communications system 300 that, according to still another embodiment of the invention, implements the above-described dual form of the UCD scheme.
- the system 300 illustratively includes a transmitting unit 305 and a receiving unit 310 .
- the transmitting unit 305 illustratively includes a plurality of filters 330 , a plurality of upconverters 340 in communication with the filters, and a plurality of transmitting antennas 345 in communication with the upconverters.
- the transmitting unit 305 further includes a DP precoder 318 , such as the familiar Tomlinson-Harashima precoder, which precodes a signal input S(t) to suppress known interference prior to transmitting the signal.
- the transmitting unit 305 further includes a processor 320 for processing the signal and a linear matrix precoder 325 that additionally precodes the signal in accordance with the dual form of the UCD scheme described above.
- the resulting vector or sequence of symbols, x k are subsequently filtered by the filters 330 and upconverted in the upconverters 340 prior to their transmission using the plurality of antennas 345 .
- the transmitted symbols are received by the receiving unit 310 .
- the receiving unit 310 illustratively includes a plurality of receiving antennas 346 , a plurality of downconverters 350 in communication with the receiving antennas, a plurality of filters 355 in communication with the downconverters, and a plurality of samplers 360 in communication with the downconverters.
- the receiving unit 310 further illustratively includes a linear equalizer 366 in communication with the plurality of samplers and a DP decoder 368 in communication with the samplers.
- the encoded signals transmitted over a channel 315 are received at the receiving unit 310 using the plurality of receiving antennas 350 .
- the received symbols are then downconverted in the downconverters 350 , filtered by the filters 355 , and sampled by the samplers 360 .
- the sampled signals are detected in the feedback equalizer 366 and the relevant information extracted in the DP decoder 368 in order to effect completion of the dual form UCD scheme.
- Yet another embodiment of the invention is a closed-loop design of WLAN based on a MIMO communications system utilizing orthogonal frequency division multiplexing, the system being defined herein as a MIMO-OFDM system.
- a MIMO-OFDM-based WLAN according to the invention, combines uniform channel decomposition, as already described, with horizontal encoding and successive, non-iterative decoding.
- the MIMO-OFDM-based WLAN incorporates both a MIMO-OFDM transmitter and a MIMO-OFDM-based WLAN.
- One embodiment of the MIMO-OFDM transmitter 400 is schematically illustrated in FIG. 4 .
- the MIMO-OFDM transmitter 400 illustratively includes a signal processor 402 for generating signal output in response to information data received from an external information source. Signal output form the signal processor 402 is supplied to a pair of convolution encoders 404 .
- the respective outputs of the convolution encoders 404 are supplied to a pair of combined interleaving and data-mapping processing units 406 , the outputs of which are fed to a precoder 408 .
- Two sets of parallel signal outputs from the precoder 408 are supplied to a pair of combined inverse discrete Fourier transform (IDFT) and cylic prefix processing units 410 .
- the resulting output of each IDFT and cylic prefix processing unit 410 is transmitted by one of a pair of transmitting antennas 412 .
- the MIMO-OFDM transmitter 400 implements horizontal encoding, according to which the respective pairs of convolution encoders 404 and interleaving and data-mapping processing units 406 form two parallel branches for separately performing encoding, bit interleaving, and data mapping.
- the data symbol of the i-th branch on the k-th subcarrier is ⁇ tilde over (x) ⁇ ik , which is the i-th element of the vector ⁇ tilde over (x) ⁇ k .
- Each precoded branch is then OFDM modulated by a corresponding one of the pair of IDFT and cylic prefix processing units 410 , each of which performs an N c -point IFFT and adds a cyclic prefix (CP) to the corresponding signal prior to its transmission.
- IDFT and cylic prefix processing units 410 each of which performs an N c -point IFFT and adds a cyclic prefix (CP) to the corresponding signal prior to its transmission.
- the MIMO-OFDM 500 illustratively includes a pair of antennas 502 which receive signals from the MIMO-OFDM transmitter 400 .
- the received signals are fed, again as parallel branches, to a pair of processing units 504 that first remove the CP and apply an N c -point FFT to each branch, respectively.
- the conditions are such that perfect, or near-perfect, synchronization, frequency offset estimation, and channel estimation can be assumed.
- the received branches are then supplied to an equalizer 506 , described more particularly below.
- the respective branches are subsequently fed from the equalizer 506 to a second pair of processing units 508 , which each perform de-interleaving and soft de-mapping on a respective branch.
- Each branch is then fed to a corresponding (soft) Viterbi decoder, denoted herein as an upper and lower branch Viterbi decoder 510 a and 510 b , respectively.
- the respective outputs of the upper and lower branch Viterbi decoders 510 a and 510 b are subsequently supplied to another processor 512 for recovering the original information transmitted from the transmitter.
- the lower branch Viterbi decoder 510 b also provides a feedback to the equalizer 506 via connection 514 .
- a key component of the closed-loop design is the precoder matrix P k applied by the precoder 408 at the transmitter 400 and the operations performed by the equalizer 506 at the receiver 500 .
- the precoder matrix P k can be determined as described above.
- the information symbols x k can then be successively detected starting with the last element of the vector.
- the matrix R k is an upper triangular matrix.
- the receiver 500 performs de-interleaving and soft de-mapping.
- a low-complexity soft Viterbi decoder can be used for each branch separately.
- the data sequence of the lower branch is detected initially to get the soft information.
- the interference due to the lower branch is subtracted from the upper branch prior to the latter being decoded.
- Interference cancellation based on a GMD can be accomplished in two stages: an initial stage and a cancellation stage.
- the lower branch data sequence can be decoded using the soft Viterbi decoder.
- the upper branch data sequence can be decoded using the soft Viterbi decoder.
- a 2 ⁇ 2 semi-unitary precoder matrix P k can be
- a precoder according to the scalar quantization scheme presented here can be represented as
- ⁇ n ⁇ ⁇ 1 ⁇ ⁇ ⁇ n 1 N 1 , 0 ⁇ n 1 ⁇ N 1 ⁇ 1, and
- ⁇ n ⁇ ⁇ 2 2 ⁇ ⁇ ⁇ ⁇ ⁇ n 2 N 2 , 0 ⁇ n 2 ⁇ N 2 31 1; N 1 and N 2 denote the quantization levels of ⁇ n1 and ⁇ n2 , respectively.
- ⁇ tilde over (Q) ⁇ k * is used in lieu of applying the original equalizer ⁇ tilde over (Q) ⁇ k * at the receiver.
- the following is a geometric approach for performing the vector quantization.
- Vector quantization can be used to quantize the precoder P( ⁇ , ⁇ ) to P( ⁇ circumflex over ( ⁇ ) ⁇ , ⁇ circumflex over ( ⁇ ) ⁇ ). Instead of transmitting the desired data vector P( ⁇ , ⁇ )x k at the transmitter, x k being an encoded data vector, P( ⁇ tilde over ( ⁇ ) ⁇ , ⁇ tilde over ( ⁇ ) ⁇ )x k is instead transmitted.
- Each P( ⁇ , ⁇ ) corresponds to a point v on the surface of the three dimensional unit sphere.
- the following steps can be used to determine the codebook.
- the codebook is iteratively updated until no further improvement in the minimum distance is observed according to the following criteria:
- the precoder P k is first mapped as a random point v on the surface of the a three dimensional unit sphere.
- the quantized vector v is obtained from the codebook with index i.
- the index i is fed back to the transmitter to reconstruct the precoder P( ⁇ circumflex over ( ⁇ ) ⁇ , ⁇ circumflex over ( ⁇ ) ⁇ ).
- the total bit number required is log 2 (N v ).
- the QR decomposition and MMSE V-BLAST algorithm can be applied to H k P( ⁇ circumflex over ( ⁇ ) ⁇ , ⁇ circumflex over ( ⁇ ) ⁇ ) when using GMD and UCD.
- the UCD scheme implemented by the system and procedures described herein incorporates a procedure referred to as a geometric mean decomposition.
- Each matrix R ( ⁇ tilde over (K) ⁇ ) has the following properties:
- the permutation matrix ⁇ is chosen to exchange the (k+1) diagonal element with any element r pp , p>k, for which r pp ⁇ ⁇ H .
- Orthogonal matrices G 1 and G 2 are subsequently constructed by modifying the elements in the identity matrix that lie at the intersection of rows k and k+1 and columns k and k+1.
- the permuted matrix ⁇ R (k) ⁇ is multiplied on the left by G 2 T and on the right by G 1 .
- the multiplications change the elements in the 2-by-2 submatrix at the intersection of rows k and k+1 with columns k and k+1.
- the choice of elements for G 1 and G 2 according to the procedure, focusing on the relevant 2-by-2 submatrices of G 2 T , ⁇ R (k) ⁇ , and G 1 are
- FIG. 6 schematically illustrates a transformation from R (k) to G 2 T ⁇ R (k) ⁇ G 1 .
- the dashed box is the 2-by-2 submatrix on the right-hand side of equation 47.
- this algorithm for the GMD requires O((M r +M t )K) flops.
- the reduction of H to bi-diagonal form using the known Golub-Reinsch bi-diagonalization scheme often the initial step in obtaining the SVD, requires O(M r M t K) flops.
- the invention as already noted can be realized in hardware, software, or a combination of hardware and software.
- the invention can be realized in a centralized fashion in one computer system, or in a distributed fashion where different elements are spread across several interconnected computer systems. Any kind of computer system or other apparatus adapted for carrying out the methods described herein is suited.
- a typical combination of hardware and software can be a general purpose computer system with a computer program that, when being loaded and executed, controls the computer system such that it carries out the methods described herein.
- the invention can be embedded in a computer program product, which comprises all the features enabling the implementation of the methods described herein, and which when loaded in a computer system is able to carry out these methods.
- Computer program in the present context means any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation; b) reproduction in a different material form.
Landscapes
- Engineering & Computer Science (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Radio Transmission System (AREA)
Abstract
Description
where Rt and Rr quantify the spatial correlations of the channel fading. The elements of the matrix, more particularly, are:
where hij denotes the channel link between the j-th transmitter antenna and the i-th receiver antenna, L denotes the channel link and T represents the sampling period.
y=HFx+z, (3)
The x is an L×1 vector of complex elements, xε L×1, representing the information symbols precoded by a linear precoder Fε M
where Tr{•} denotes the trace of a matrix. It should be noted that because a more general frequency-selective channel can be represented by a spatial-time channel with larger dimensionality, Equation 3, accordingly, provides a general representation of the
where |•| denotes the determinant of a matrix. If the channel state information at the transmitter (CSIT) and the channel state information at the receiver (CSIR) are both available, the channel capacity can be maximized with respect to a linear precoder F given the input power constraint σx 2Tr{FF*}≦P; that is,
where, from equation 4,
and CIT is the charnel capacity of an “informed transmitter.”
with μ being chosen such that
The solution to equation 6, therefore, is
H=QRP*, (9)
where Rε K×K is an upper triangular matrix, the equal diagonal elements of which are defined as
and where Qε M×K and Pε N×K are each semi-unitary matrices whose columns are orthonormal with one another. A computationally efficient and numerically stable algorithm for effecting the decomposition reflected in equation 9 is provided below.
{tilde over (F)}=VΦ1/2Ω*. (10)
The first term on the left-hand side of equation (1), V, is a unitary matrix indirectly derived by performing an SVD of the channel matrix, H, which as already described yields the following:
H=UΛV*,
where the middle term, Λ, is a K×K matrix whose diagonal elements {λH,k}k=1 K are the nonzero singular values of H. The first term on the left-hand side of equation 10, V, accordingly is the conjugate transpose of V*.
The last term on the left-hand side of equation 10, Ω, is a real-valued L×K matrix, such that L≧K and Ω*Ω=I. The introduction of the L×K matrix, Ω, is one step leading to the UCD. As will be apparent from the following discussion, introduction of Ω provides several distinct advantages. Firstly, however, the design of Ω is described.
where Σ=Λφ1/2 is a diagonal matrix, the diagonal elements of which are {σi} i=1 K.
A semi-unitary matrix Ωε L×K is found such that a standard QR decomposition of Ga yields an upper triangular matrix having equal diagonal elements. This is more particularly demonstrated by rewriting the augmented matrix, Ga, as follows:
where Ω0ε L×L is a unitary matrix. The matrix Ω is formed from the first K columns of the matrix Ω0. The augmented matrix Ga can be further rewritten as
where RJε L×L is an upper triangular matrix with equal diagonal elements, QJε (M
Setting Ω0=P*J and
it follows that equation 16 can be rewritten as Ga=QG
wi=rJ,ii −1qG
where rJ,ii is the ith diagonal element of RJ and qG
it follows that the diagonal elements λA,i and λB,i of ΛA and ΛB, respectively, satisfy λA,i=√{square root over (λB,i 2+α)}, i=1, 2, . . . , N.
Accordingly the SVD of J, above, is
where {tilde over (Σ)} is an L-by-L diagonal matrix with the following diagonal elements
{tilde over (σ)}i=√{square root over (σi 2+α)}, 1≦i≦K (22a)
and
{tilde over (σ)}i=√{square root over (α)}, K=1≦i≦L. (22b)
Performing a GMD of {tilde over (Σ)} yields
{tilde over (Σ)}=(Q 1 Q 2 . . . Q L-1)R J(P L-1 T P L-2 T . . . P 1 T) (23)
Hence, it follows that
Therefore the linear precoder, {tilde over (F)}, has the following form:
{tilde over (F)}=V[Φ1/2 0K×(L-K)]P 1P2 . . . PL-1. (25)
Moreover, the matrix, QG
QG
vM
for i=Mt:−1:1
{circumflex over (x)}i=wi*vi(nulling step)
{tilde over (x)}i=C[{circumflex over (x)}i]
v i-1 =v i −h i {tilde over (x)} i(cancellation step)
end,
where C represents a mapping to the nearest symbol of a predefined symbol constellation.
Instead of the
y=H*x+z, (28)
where H* is the conjugate transpose of the previously described channel matrix, x is the transmitted signal symbol, and z denotes the channel noise assumed to have a particular distribution (e.g., additive white Gaussian noise). The reversal yields a precoder Frev and, with respect to cancellation, an equalizer {wi}i=1 L. Normalizing the {wi}i=1 L to correspond to the unit Euclidean norm yields {
y=F rev *HWD q x+z, (29)
where the i-th scalar subchannel of the MIMO channel is
By applying a dirty, paper (DP) precoder to xi and treating
as the interference known at the transmitter, the following equivalent subchannel is obtained
having the following SNIR
It can easily be shown that qi>0, for 0≦i≦L. Moreover, it can be proven that
y k H k P k x k +z k , k=1, 2, . . . , N, (33)
where the noise component is zk˜N(0, σz 2I); the noise component is assumed to be circularly symmetric Gaussian noise. The received branches are then supplied to an
Hk=QkRkPk*, (34)
from which the precoder matrix Pk is determined. The precoder matrix is fed back to the
y k =Q k R k x k +z k , k=1, 2, . . . , N. (35)
{tilde over (y)} k R k x k +{tilde over (z)} k,
where Rk=Qk*HkPk is a 2×2 upper triangular matrix with constant diagonal elements and zk˜N(0,σz 2I). The information symbols xk can then be successively detected starting with the last element of the vector.
Note that the σ2k 2 and {circumflex over (x)}2k values provide the soft information of the lower branch. The lower branch data sequence can be decoded using the soft Viterbi decoder.
where the σ1k 2 and {circumflex over (x)}1k values provide the soft information for the upper branch;
The two methods can be utilized for quantization: scalar quantization and vector quantization.
where
0≦n1≦N1−1, and
0≦n2≦N231 1; N1 and N2 denote the quantization levels of θn1 and φn2, respectively. After obtaining the precoder matrix Pk using the UCD scheme, the precoder Pk can be quantized to the “closest” grid point. Thus only the index (n1,n2) needs to be fed back to the transmitter. The total bit number required, therefore, is log2(n1,n2). To reduce the effect of quantization error, {tilde over (Q)}k* is used in lieu of applying the original equalizer {tilde over (Q)}k* at the receiver. {tilde over (Q)}k* is obtained via a QR decomposition:
HkP(θn1,φn2){tilde over (Q)}k{tilde over (R)}k, k=1, . . . , N. (42)
d=∥P(θ,φ)x k −P({tilde over (θ)},{tilde over (φ)})x k∥2 =x k *[P(θ,φ)−P({tilde over (θ)},{tilde over (φ)})]*[P(θ,φ)−P({tilde over (θ)},{tilde over (φ)})]x k, (43)
where ∥•∥ is the Euclidean norm. Moreover, by straightforward algebraic manipulation
[P(θ,φ)−P({tilde over (θ)},{tilde over (φ)})]*[P(θ,φ)−P({tilde over (θ)},{tilde over (φ)}]=2I 2−2[cos θ cos {tilde over (θ)}+sin θ sin {tilde over (θ)} cos(φ−{circumflex over (φ)})]I 2, (44)
where I2 is the identity matrix of
d=(2−2 cos ψ)=∥v−{circumflex over (v)}∥ 2. (46)
-
- 1. The nearest neighbor condition (NNC). For a given codebook {
v t}i=1 Nv, assign vn to the i-th region:
- 1. The nearest neighbor condition (NNC). For a given codebook {
-
-
- where Si, i=1, 2, . . . , Nv, is the partition set for the i-th code vector; and
- 2. The centroid condition (CC). For a given partition, Si, the optimum code vectors {
v i}i=1 Nv satisfy
-
It can be shown that the solution to the above optimization problem is
where
is the mean vector for the partition set Si, i=1, 2, . . . , Nv.
- (a) rij ({tilde over (K)})=0, if i≧j or j≧max{{tilde over (K)},i}, and
- (b) rii ({tilde over (K)})=
λ H for all i<{tilde over (K)}.
The geometric mean of rii ({tilde over (K)}), K≦i≦K, isλ H.
If δ1=δ2=
Note that since
c 2 +s 2=1 and (cδ 1)2+(sδ 2)2=
The validity of equation 47 follows by direct computation with the above identities. Defining Qk=ΠG2 and Pk=ΠG1, the matrix R(k+1) is set equal to Qk TR(k)Pk:
R(k+1)=Qk TR(k)Pk. (49)
It follows from
R (K)=(Q K-1 T . . . Q 2 T Q 1 T)Σ(P 1 P 2 . . . P 1). (50)
H=QRP* is obtained by combining the identity 50 with the singular value decomposition, where
Claims (19)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US11/718,506 US7711066B2 (en) | 2004-11-05 | 2005-11-04 | Uniform channel decomposition for MIMO communications |
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US62552504P | 2004-11-05 | 2004-11-05 | |
US11/718,506 US7711066B2 (en) | 2004-11-05 | 2005-11-04 | Uniform channel decomposition for MIMO communications |
PCT/US2005/040294 WO2006052890A1 (en) | 2004-11-05 | 2005-11-04 | Uniform channel decomposition for mimo communications |
Publications (2)
Publication Number | Publication Date |
---|---|
US20080112504A1 US20080112504A1 (en) | 2008-05-15 |
US7711066B2 true US7711066B2 (en) | 2010-05-04 |
Family
ID=35810379
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
US11/718,506 Active US7711066B2 (en) | 2004-11-05 | 2005-11-04 | Uniform channel decomposition for MIMO communications |
Country Status (6)
Country | Link |
---|---|
US (1) | US7711066B2 (en) |
EP (1) | EP1807959A1 (en) |
KR (1) | KR20070085471A (en) |
CN (1) | CN101142780A (en) |
CA (1) | CA2587770A1 (en) |
WO (1) | WO2006052890A1 (en) |
Cited By (15)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20090086850A1 (en) * | 2007-09-28 | 2009-04-02 | Ahmadreza Rofougaran | Method and system for a receiver with undersampling mixing using multiple clock phases |
US20090122889A1 (en) * | 2007-11-09 | 2009-05-14 | Samsung Electronics Co., Ltd. | Method and apparatus for decomposing channel in closed-loop multiple input multiple output communication system |
US20090203335A1 (en) * | 2007-04-26 | 2009-08-13 | Samsung Electronics Co. Ltd. | Apparatus and method for partial adaptive transmission in multiple-input multiple-output system |
US20100061482A1 (en) * | 2006-11-02 | 2010-03-11 | Moon Il Lee | Method for transmitting data using phase shift based precoding and transceiver supporting the same |
US20100067605A1 (en) * | 2007-04-30 | 2010-03-18 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and Arrangement for Adapting a Multi-Antenna Transmission |
US20100166119A1 (en) * | 2008-12-30 | 2010-07-01 | Jiacheng Wang | Mimo symbol decoder and method for decoding spatially multiplexed symbols using combined linear equalization and maximum likelihood decoding |
US20110051828A1 (en) * | 2007-01-09 | 2011-03-03 | Mark Kent | Method and system for an efficient channel quantization method for mimo pre-coding systems |
US20110164700A1 (en) * | 2008-07-07 | 2011-07-07 | Wi-Lan, Inc. | Closed form singular value decomposition |
US20110200141A1 (en) * | 2007-01-09 | 2011-08-18 | Mark Kent | Method and system for an efficient channel quantization method for mimo pre-coding systems |
US8654876B2 (en) | 2008-12-04 | 2014-02-18 | Samsung Electronics Co., Ltd. | Transmitting apparatus in multiple input multiple output system |
US20150003557A1 (en) * | 2013-06-26 | 2015-01-01 | Massachusetts Institute Of Technology | Permute Codes, Iterative Ensembles, Graphical Hash Codes, And Puncturing Optimization |
US9143175B2 (en) | 2011-02-17 | 2015-09-22 | Massachusetts Institute Of Technology | Rateless and rated coding using spinal codes |
US9160399B2 (en) | 2012-05-24 | 2015-10-13 | Massachusetts Institute Of Technology | System and apparatus for decoding tree-based messages |
EP3404881A4 (en) * | 2016-03-21 | 2019-02-20 | Huawei Technologies Co., Ltd. | Signal to noise ratio (snr) processing method, apparatus and system |
US10659138B1 (en) | 2018-12-04 | 2020-05-19 | Huawei Technologies Co., Ltd. | System and method for precoding in a line of sight (LOS) multiple-input multiple-output (MIMO) communication system |
Families Citing this family (55)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7616695B1 (en) | 2004-06-17 | 2009-11-10 | Marvell International Ltd. | MIMO equalizer design: an algorithmic perspective |
US7978759B1 (en) * | 2005-03-24 | 2011-07-12 | Marvell International Ltd. | Scalable equalizer for multiple-in-multiple-out (MIMO) wireless transmission |
US7813421B2 (en) | 2006-01-17 | 2010-10-12 | Marvell World Trade Ltd. | Order recursive computation for a MIMO equalizer |
US20070189151A1 (en) * | 2006-02-10 | 2007-08-16 | Interdigital Technology Corporation | Method and apparatus for performing uplink transmission in a multiple-input multiple-output single carrier frequency division multiple access system |
US7664200B2 (en) * | 2006-02-24 | 2010-02-16 | Broadcom Corporation | Method and system for minimizing effects of transmitter impairments in multiple input multiple output (MIMO) beamforming communication systems |
US7991090B2 (en) * | 2006-05-04 | 2011-08-02 | Broadcom Corporation | Method and system for reordered QRV-LST (layered space time) detection for efficient processing for multiple input multiple output (MIMO) communication systems |
US8472565B2 (en) * | 2006-05-23 | 2013-06-25 | Lg Electronics Inc. | Apparatus for processing received signal, method thereof, and method for selecting mapping rule |
US20080002601A1 (en) * | 2006-06-30 | 2008-01-03 | Coronel Pedro E | Method and apparatus for relaying spatially-multiplexed signals |
KR100992418B1 (en) * | 2006-07-12 | 2010-11-05 | 삼성전자주식회사 | Apparatus and method for removing of interference in multi antenna system transmitter |
US7839835B2 (en) | 2006-08-22 | 2010-11-23 | Nec Laboratories America, Inc. | Quantized precoding over a set of parallel channels |
KR100895101B1 (en) | 2006-10-11 | 2009-04-28 | 한국전자통신연구원 | Apparearus and method for synchronization channel transmission in wireless communication system |
KR100888500B1 (en) | 2006-11-01 | 2009-03-12 | 한국전자통신연구원 | Apparearus and method for synchronization channel and broadcast channel transmission in wireless communication system |
US7961775B2 (en) * | 2007-01-09 | 2011-06-14 | Broadcom Corporation | Method and system for a delta quantizer for MIMO pre-coders with finite rate channel state information feedback |
US7983322B2 (en) * | 2007-01-09 | 2011-07-19 | Broadcom Corporation | Method and system for codebook design of MIMO pre-coders with finite rate channel state information feedback |
CN101222259B (en) * | 2007-01-09 | 2013-01-16 | 中兴通讯股份有限公司 | Codebook type precoding method used for four-transmitting antenna MIMO system |
US8090049B2 (en) | 2007-02-12 | 2012-01-03 | Broadcom Corporation | Method and system for an alternating delta quantizer for limited feedback MIMO pre-coders |
US8090048B2 (en) * | 2007-02-12 | 2012-01-03 | Broadcom Corporation | Method and system for an alternating channel delta quantizer for MIMO pre-coders with finite rate channel state information feedback |
US8077796B2 (en) * | 2007-03-05 | 2011-12-13 | Intel Corporation | Methods and arrangements for communicating in a multiple input multiple output system |
KR101382894B1 (en) | 2007-03-12 | 2014-04-08 | 엘지전자 주식회사 | Method for transmitting control information in multiple antenna system |
KR100926663B1 (en) | 2007-05-10 | 2009-11-17 | 연세대학교 산학협력단 | Bidirectional Multi-antenna Communication Using Virtual Channel |
KR101375732B1 (en) * | 2007-11-21 | 2014-03-19 | 연세대학교 산학협력단 | Apparatus and method for eliminating frequency synchronization error in relay wireless commnication system |
KR100991794B1 (en) | 2007-12-31 | 2010-11-03 | 엘지전자 주식회사 | Method For Reducing Inter-Cell Interference |
US8064849B2 (en) * | 2008-02-07 | 2011-11-22 | Telefonaktiebolaget Lm Ericsson (Publ) | Precoding for multiple anntennas |
EP2120412A1 (en) * | 2008-05-14 | 2009-11-18 | SIDSA (Semiconductores Investigación) Y Diseño SA | System and transceiver for DSL communications based on single carrier modulation, with efficient vectoring, capacity approaching channel coding structure and preamble insertion for agile channel adaption |
EP2141825A1 (en) * | 2008-06-30 | 2010-01-06 | Alcatel, Lucent | Method of reducing intra-cell spatial interference in a mobile cellular network |
WO2010005999A2 (en) * | 2008-07-07 | 2010-01-14 | Wi-Lan, Inc. | Multiple input multiple output (mimo) rank adaptation with uniform channel decomposition |
US8320510B2 (en) * | 2008-09-17 | 2012-11-27 | Qualcomm Incorporated | MMSE MIMO decoder using QR decomposition |
US8175189B2 (en) * | 2009-03-11 | 2012-05-08 | Hitachi, Ltd. | Fast generalized decision feedback equalizer precoder implementation for multi-user multiple-input multiple-output wireless transmission systems |
BR112012003477A2 (en) * | 2009-08-17 | 2017-05-23 | Alcatel Lucent | "method for maintaining coherence of a precoding channel in a communication network and associated apparatus." |
EP2474104B1 (en) * | 2009-09-04 | 2015-02-11 | Hitachi, Ltd. | Tomlinson harashima precoding with additional receiver processing in a multi-user multiple-input multiple-output wireless transmission system |
CN102025405A (en) * | 2009-09-17 | 2011-04-20 | 中兴通讯股份有限公司 | Combined receiving and transmitting terminal information based multi-beam forming method and system |
CN101764772B (en) * | 2009-10-26 | 2013-07-31 | 广州杰赛科技股份有限公司 | Channel equalization method and communication system thereof based on precoding |
KR101587566B1 (en) | 2009-12-30 | 2016-02-02 | 삼성전자주식회사 | Apparatus and method for unitary precoding in mu-mimo system |
CN102014089B (en) * | 2010-11-29 | 2013-11-27 | 北京星河亮点技术股份有限公司 | Space-time pre-equilibrium method and device based on time reversal multi-aerial system |
EP2458747A1 (en) * | 2010-11-30 | 2012-05-30 | ST-Ericsson SA | Detection process for a receiver of a wireless MIMO communication system |
US8981993B2 (en) * | 2011-04-27 | 2015-03-17 | Telefonaktiebolaget L M Ericsson (Publ) | Beamforming methods and apparatuses |
CN102918781B (en) * | 2011-06-03 | 2015-03-25 | 华为技术有限公司 | Pre-coding method and transmitter used in distributed multiple input multiple output system |
KR101880990B1 (en) * | 2011-11-16 | 2018-08-24 | 삼성전자주식회사 | Method and apparatus for transmitting and receiving signals in multi-antenna system |
TWI469558B (en) * | 2013-01-29 | 2015-01-11 | Nat Univ Chung Hsing | Low complexity pre-coding method |
WO2014169048A1 (en) * | 2013-04-09 | 2014-10-16 | Interdigital Patent Holdings, Inc. | Joint precoding and multivariate backhaul compression for the downlink of cloud radio access networks |
US9450787B2 (en) * | 2014-01-24 | 2016-09-20 | Huawei Technologies Co., Ltd. | System and method for early termination in iterative null-space directed singular value decomposition for MIMO |
CN104023400B (en) * | 2014-05-23 | 2018-01-19 | 广州海格通信集团股份有限公司 | For the down channel allocation method based on demand of OFDM base station systems |
CN105871503B (en) * | 2015-01-22 | 2019-03-12 | 华邦电子股份有限公司 | Multiple input, multiple output wireless communication system and its channel decomposition method |
CN106341152B (en) * | 2015-07-08 | 2019-02-05 | 中国科学院微电子研究所 | A kind of radio-frequency front-end, transmitting terminal, receiving end and MIMO communication system |
WO2017008308A1 (en) * | 2015-07-16 | 2017-01-19 | 华为技术有限公司 | Method of increasing transmission rate and device utilizing same |
US9590708B1 (en) * | 2015-08-25 | 2017-03-07 | Motorola Mobility Llc | Method and apparatus for equal energy codebooks for antenna arrays with mutual coupling |
EP3188427B1 (en) * | 2015-12-28 | 2019-08-21 | Institut Mines-Télécom | Reordered sub-block decoding |
US10236958B2 (en) * | 2016-03-21 | 2019-03-19 | University Of Science And Technology Of China | Method for signal transmission to multiple user equipments utilizing reciprocity of wireless channel |
EP3229429B1 (en) * | 2016-04-08 | 2021-03-03 | Institut Mines-Télécom | Methods and devices for symbols detection in multi antenna systems |
US10743025B2 (en) * | 2016-09-01 | 2020-08-11 | Lg Electronics Inc. | Method and apparatus for performing transformation using layered givens transform |
EP3404843B1 (en) * | 2017-05-17 | 2022-12-07 | Mitsubishi Electric R&D Centre Europe B.V. | Method for enabling both analog and digital beamforming |
KR102383100B1 (en) | 2017-09-25 | 2022-04-05 | 삼성전자주식회사 | Wireless communication appartus for adaptive beamforming and method of operation thereof |
CN109743090A (en) * | 2018-12-10 | 2019-05-10 | 深圳市海派通讯科技有限公司 | A kind of fast algorithm of non-code book linear predictive coding |
CN111371478B (en) | 2018-12-26 | 2021-10-15 | 华为技术有限公司 | Precoding method and device and information transmission method and device |
US11159208B1 (en) * | 2020-07-15 | 2021-10-26 | Samsung Electronics Co., Ltd | Optimal precoder method and apparatus with equal power allocation |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20030048856A1 (en) * | 2001-05-17 | 2003-03-13 | Ketchum John W. | Method and apparatus for processing data for transmission in a multi-channel communication system using selective channel inversion |
US6937843B2 (en) * | 2001-12-05 | 2005-08-30 | Lucent Technologies Inc. | Wireless communication system with interference compensation |
US7209522B1 (en) * | 2002-12-12 | 2007-04-24 | Marvell International Ltd. | Blast MIMO signal processing method and apparatus |
-
2005
- 2005-11-04 US US11/718,506 patent/US7711066B2/en active Active
- 2005-11-04 KR KR1020077011983A patent/KR20070085471A/en not_active Application Discontinuation
- 2005-11-04 EP EP05824329A patent/EP1807959A1/en not_active Withdrawn
- 2005-11-04 WO PCT/US2005/040294 patent/WO2006052890A1/en active Search and Examination
- 2005-11-04 CA CA002587770A patent/CA2587770A1/en not_active Abandoned
- 2005-11-04 CN CNA2005800423895A patent/CN101142780A/en active Pending
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20030048856A1 (en) * | 2001-05-17 | 2003-03-13 | Ketchum John W. | Method and apparatus for processing data for transmission in a multi-channel communication system using selective channel inversion |
US6937843B2 (en) * | 2001-12-05 | 2005-08-30 | Lucent Technologies Inc. | Wireless communication system with interference compensation |
US7209522B1 (en) * | 2002-12-12 | 2007-04-24 | Marvell International Ltd. | Blast MIMO signal processing method and apparatus |
Non-Patent Citations (5)
Title |
---|
Ginis et al, "A multi-user PRecoding Scheme achieving Crosstalk Cancellation with Application to DSL Systems," Signals, Systems and Computers, 2000. Conference Record of the Thirty-Fourth Asilomar Conference on Oct. 29-Nov. 1, 2000, Piscataway, NJ, USA, IEEE, vol. 2, Oct. 29, 2000, pp. 1627-1631, XP010535274 ISBN: 0-7803-6514-3. * |
Jiang et al., Joint Transceiver Design for MIMO Communications Using Geometric Mean Decomposition, submitted to IEEE Transactions on Signal Processing, Mar. 2004, http://www.sal.ufl.edu/yjiang/papers/gmdCommR2.pdf, retrieved Feb. 22, 2006. |
Jiang et al., MIMO Transceiver Design Using Geometric Mean Deomposition, IEEE Information Theory Workshop, San Antonio, TX, pp. 193-197, Oct. 24-29, 2004. |
Love et al., Limited Feedback Precoding for Spatial Multiplexing Systems, IEEE Global Communications Conference, San Francisco, CA, vol. 7, pp. 1857-1861, Dec. 1-5, 2003. |
Sampath et al., Generalized Linear Precoder and Decoder Design for MIMO Channels Using the Weighted MMSE Criterion, Dec. 2001, IEEE Transactions on Communications, vol. 49, pp. 2198-2206. * |
Cited By (31)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20100061482A1 (en) * | 2006-11-02 | 2010-03-11 | Moon Il Lee | Method for transmitting data using phase shift based precoding and transceiver supporting the same |
US8175182B2 (en) * | 2006-11-02 | 2012-05-08 | Lg Electronics Inc. | Method for transmitting data using phase shift based precoding and transceiver supporting the same |
US20110200141A1 (en) * | 2007-01-09 | 2011-08-18 | Mark Kent | Method and system for an efficient channel quantization method for mimo pre-coding systems |
US8085833B2 (en) * | 2007-01-09 | 2011-12-27 | Broadcom Corporation | Method and system for an efficient channel quantization method for MIMO pre-coding systems |
US20110051828A1 (en) * | 2007-01-09 | 2011-03-03 | Mark Kent | Method and system for an efficient channel quantization method for mimo pre-coding systems |
US7953138B2 (en) * | 2007-01-09 | 2011-05-31 | Broadcom Corporation | Method and system for an efficient channel quantization method for MIMO pre-coding systems |
US8467467B2 (en) * | 2007-04-26 | 2013-06-18 | Samsung Electronics Co., Ltd. | Apparatus and method for partial adaptive transmission in multiple-input multiple-output system |
US20090203335A1 (en) * | 2007-04-26 | 2009-08-13 | Samsung Electronics Co. Ltd. | Apparatus and method for partial adaptive transmission in multiple-input multiple-output system |
US8306140B2 (en) * | 2007-04-30 | 2012-11-06 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and arrangement for adapting a multi-antenna transmission |
US20140294112A1 (en) * | 2007-04-30 | 2014-10-02 | Telefonaktiebolaget L M Ericsson (Publ) | Method and Arrangement for Adapting a Multi-Antenna Transmission |
US10609577B2 (en) | 2007-04-30 | 2020-03-31 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and arrangement for adapting a multi-antenna transmission |
US20100067605A1 (en) * | 2007-04-30 | 2010-03-18 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and Arrangement for Adapting a Multi-Antenna Transmission |
US10051492B2 (en) | 2007-04-30 | 2018-08-14 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and arrangement for adapting a multi-antenna transmission |
US9419695B2 (en) | 2007-04-30 | 2016-08-16 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and arrangement for adapting a multi-antenna transmission |
US9077401B2 (en) * | 2007-04-30 | 2015-07-07 | Telefonaktiebolaget L M Ericsson (Publ) | Method and arrangement for adapting a multi-antenna transmission |
US20090086850A1 (en) * | 2007-09-28 | 2009-04-02 | Ahmadreza Rofougaran | Method and system for a receiver with undersampling mixing using multiple clock phases |
US8514997B2 (en) * | 2007-09-28 | 2013-08-20 | Broadcom Corporation | Method and system for a receiver with undersampling mixing using multiple clock phases |
US20090122889A1 (en) * | 2007-11-09 | 2009-05-14 | Samsung Electronics Co., Ltd. | Method and apparatus for decomposing channel in closed-loop multiple input multiple output communication system |
US8238464B2 (en) * | 2007-11-09 | 2012-08-07 | Samsung Electronics Co., Ltd. | Method and apparatus for decomposing channel in closed-loop multiple input multiple output communication system |
US8320492B2 (en) * | 2008-07-07 | 2012-11-27 | Wi-Lan Inc. | Closed form singular value decomposition |
US20110164700A1 (en) * | 2008-07-07 | 2011-07-07 | Wi-Lan, Inc. | Closed form singular value decomposition |
US8654876B2 (en) | 2008-12-04 | 2014-02-18 | Samsung Electronics Co., Ltd. | Transmitting apparatus in multiple input multiple output system |
US8194798B2 (en) * | 2008-12-30 | 2012-06-05 | Intel Corporation | MIMO symbol decoder and method for decoding spatially multiplexed symbols using combined linear equalization and maximum likelihood decoding |
US20100166119A1 (en) * | 2008-12-30 | 2010-07-01 | Jiacheng Wang | Mimo symbol decoder and method for decoding spatially multiplexed symbols using combined linear equalization and maximum likelihood decoding |
US9143175B2 (en) | 2011-02-17 | 2015-09-22 | Massachusetts Institute Of Technology | Rateless and rated coding using spinal codes |
US9160399B2 (en) | 2012-05-24 | 2015-10-13 | Massachusetts Institute Of Technology | System and apparatus for decoding tree-based messages |
US9793944B2 (en) | 2012-05-24 | 2017-10-17 | Massachusetts Institute Of Technology | System and apparatus for decoding tree-based messages |
US20150003557A1 (en) * | 2013-06-26 | 2015-01-01 | Massachusetts Institute Of Technology | Permute Codes, Iterative Ensembles, Graphical Hash Codes, And Puncturing Optimization |
US9270412B2 (en) * | 2013-06-26 | 2016-02-23 | Massachusetts Institute Of Technology | Permute codes, iterative ensembles, graphical hash codes, and puncturing optimization |
EP3404881A4 (en) * | 2016-03-21 | 2019-02-20 | Huawei Technologies Co., Ltd. | Signal to noise ratio (snr) processing method, apparatus and system |
US10659138B1 (en) | 2018-12-04 | 2020-05-19 | Huawei Technologies Co., Ltd. | System and method for precoding in a line of sight (LOS) multiple-input multiple-output (MIMO) communication system |
Also Published As
Publication number | Publication date |
---|---|
WO2006052890A1 (en) | 2006-05-18 |
CN101142780A (en) | 2008-03-12 |
US20080112504A1 (en) | 2008-05-15 |
CA2587770A1 (en) | 2006-05-18 |
KR20070085471A (en) | 2007-08-27 |
EP1807959A1 (en) | 2007-07-18 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US7711066B2 (en) | Uniform channel decomposition for MIMO communications | |
US7561632B1 (en) | Beamforming techniques for MIMO communication systems | |
Jiang et al. | Joint transceiver design for MIMO communications using geometric mean decomposition | |
US9071295B1 (en) | Method and apparatus for receiving signals in a MIMO system with multiple channel encoders | |
US7813458B2 (en) | System and method for precoding in a multiple-input multiple-output (MIMO) system | |
US8249186B2 (en) | Method and apparatus for singular value decomposition of a channel matrix | |
US20060039489A1 (en) | Method and apparatus for providing closed-loop transmit precoding | |
US20090075686A1 (en) | Method and apparatus for wideband transmission based on multi-user mimo and two-way training | |
US8081692B1 (en) | Transmit beamforming utilizing codebook selection in a wireless MIMO communication system | |
US20110096858A1 (en) | Mimo decoding system and method | |
US8953702B2 (en) | Precoding matrix index selection process for a MIMO receiver based on a near-ML detection, and apparatus for doing the same | |
US10250360B2 (en) | Methods and devices for sub-block decoding data signals | |
US10116326B2 (en) | Semi-exhaustive recursive block decoding method and device | |
US10284334B2 (en) | Methods and devices for sequential sphere decoding | |
Dang et al. | MMSE beamforming for SC-FDMA transmission over MIMO ISI channels | |
US10560222B2 (en) | Methods and devices for sub-block decoding data signals | |
Zimaglia et al. | A novel deep learning approach to csi feedback reporting for nr 5g cellular systems | |
US8576959B2 (en) | Receiver with prefiltering for discrete fourier transform-spread-orthogonal frequency division multiplexing (DFT-S-OFDM) based systems | |
EP3664333B1 (en) | Devices and methods for parallelized recursive block decoding | |
Maleki et al. | Precoding Design and PMI Selection for BICM-MIMO Systems with 5G New Radio Type-I CSI | |
Jiang et al. | Applying the Geometric Mean Decomposition in Joint Transceiver Design for Multi-Input Multi-Output (MIMO) Communications | |
Tuan et al. | Error-entropy based channel state estimation of spatially correlated MIMO-OFDM |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AS | Assignment |
Owner name: UNIVERSITY OF FLORIDA RESEARCH FOUNDATION, INC., F Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:JIANG, YI;LI, JIAN;REEL/FRAME:018040/0915;SIGNING DATES FROM 20060428 TO 20060512 Owner name: UNIVERSITY OF FLORIDA RESEARCH FOUNDATION, INC.,FL Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:JIANG, YI;LI, JIAN;SIGNING DATES FROM 20060428 TO 20060512;REEL/FRAME:018040/0915 |
|
STCF | Information on status: patent grant |
Free format text: PATENTED CASE |
|
CC | Certificate of correction | ||
FPAY | Fee payment |
Year of fee payment: 4 |
|
AS | Assignment |
Owner name: NATIONAL SCIENCE FOUNDATION, VIRGINIA Free format text: CONFIRMATORY LICENSE;ASSIGNOR:UNIVERSITY OF FLORIDA;REEL/FRAME:035503/0064 Effective date: 20140717 |
|
MAFP | Maintenance fee payment |
Free format text: PAYMENT OF MAINTENANCE FEE, 8TH YR, SMALL ENTITY (ORIGINAL EVENT CODE: M2552) Year of fee payment: 8 |
|
MAFP | Maintenance fee payment |
Free format text: PAYMENT OF MAINTENANCE FEE, 12TH YR, SMALL ENTITY (ORIGINAL EVENT CODE: M2553); ENTITY STATUS OF PATENT OWNER: SMALL ENTITY Year of fee payment: 12 |